# Comparing groups based on data containing proportions without raw counts

I have 2 object types, A and B

For type A, I observe delivery to demographic groups x1, x2, x3, x4.... xn. For type B, I observe delivery to the same demographic groups x1, x2, x3, x4.... xn.

x1(a) + x2(a) + x3(a) + .. xn(a) = 100, where a is a sample of type A.

x1(b) + x2(b) + x3(b) + .. xn(b) = 100 where b is a sample of type B.

Each delivery, xi(a) or xi(b) is a percentage value between 0 - 100.

The raw counts are not available.

I have 5000 samples for delivery of type A I have 13000 samples for delivery of type B

I want to compare the delivery to the same audience group for different object types, i.e compare the distribution of A's delivery to x1 and B's delivery to x1, i.e 5000 samples of x1 from A with 13000 samples of x1 of B. Is such a comparison statistically reasonable? Can I use a 2 sample Z test for proportions here?

I want to compare the delivery to different audience groups for the same object type, i.e compare the distribution of A's delivery to x1 and A's delivery to x2, i.e 5000 samples of x1 with 5000 samples of x2 in A. Is such a comparison statistically reasonable? Can I use a 2 sample Z test for proportions here?

Are there any other tests that you'd think are reasonable given this information and that I am dealing with proportions and not raw counts? Suggestions of both parametric and non-parametric tests are appreciated.

• I don't understand your description of what is known and what is not known. Could you display a small data table giving examples of rows, columns, and what's in each cell? May 1, 2023 at 20:54
• @rolando2I just fixed the question. Hope this helps! Thanks. May 2, 2023 at 21:54